rationalzie the denominator 4 upon root 5 +root 3
Answers
Step-by-step explanation:
By rationalizing the denominator of \frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}
48
+
18
4
3
+5
2
we get
\bold{\frac{9+4 \sqrt{6}}{15}}
15
9+4
6
Step-by-step explanation:
Rationalizing the denominator means multiplying the numerator in a fraction by the value of the denominator but by its opposite signed value.
Now to rationalize the above figure we multiply both the numerator and denominator by [√48-√18]
\left[\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}\right]\left[\frac{\sqrt{48}-\sqrt{18}}{\sqrt{48}-\sqrt{18}}\right][
48 + 18
4
3
+5
2
][
48 − 18
48 − 18 ]
On removing the brackets and multiplying,
The denominator is multiplied by using the formula \bold{(a+b)(a-b)=a^{2}-b^{2}}(a+b)(a−b)=a
2
−b
2
\begin{gathered}\begin{aligned} &=\left[\frac{4 \sqrt{3}(\sqrt{48}-\sqrt{18})+5 \sqrt{2}(\sqrt{48}-\sqrt{18})}{48-18}\right] \\ &=\left[\frac{4 \sqrt{3}(\sqrt{48}-\sqrt{18})+5 \sqrt{2}(\sqrt{48}-\sqrt{18})}{30}\right] \\ &=\left[\frac{4 \sqrt{3} \sqrt{48}-4 \sqrt{3} \sqrt{18}+5 \sqrt{2} \sqrt{48}-5 \sqrt{2} \sqrt{18}}{30}\right] \\ &=\left[\frac{18+8 \sqrt{6}}{30}\right] \end{aligned}\end{gathered}
=[
48−18
4
3
( 48 − 18 )+5
2
( 48− 18 ) ]
=[ 30
4
3
( 48− 18 )+5
2
( 48 − 18 )]
=[ 30
4
3
48
−4
3
18
+5
2
48
−5
2
18
]
=[
30
18+8
6
]
By rationalizing the denominator of \frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}
48
+
18
4
3
+5
2
we get
\bold{\frac{9+4 \sqrt{6}}{15}}
15
9+4
6
as the answer.
Answer:
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